柴式法生長氧化鋁單晶過程最佳化熱流場之分析

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姓名

陳建宏(Chien-Hung Chen) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

柴式法生長氧化鋁單晶過程最佳化熱流場之分析
(Thermal-fluid Analysis during the Sapphire crystal growth process by using the Cz method)

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摘要(中)

CZ長晶法生長氧化鋁單晶過程中，為了提升氧化鋁單晶的生長品質，必須了解CZ長晶爐內部的熱傳與熔湯流動情形。由於單晶生長過程無法直接觀察熔湯內的熱流場分佈，所以本研究使用有限元素法之COMSOL軟體模擬電磁場、熱場與流場三場耦合之氧化鋁單晶生長過程。RF線圈產生感應電磁場，銥坩堝受到感應電磁場而產生熱源，銥坩堝熱源傳遞到長晶爐內部產生熱場及流場。
本研究主要模擬CZ法生長氧化鋁單晶的生長過程，探討生長過程中熔湯內的熱流場、功率趨勢與晶體固液介面溫梯。為了找出理想的長晶參數，本研究探討不同線圈位置、不同底部絕熱層與不同線圈形狀。以最佳長晶參數做為基準模擬理想氧化鋁單晶生長過程。
結果呈現氧化鋁單晶生長過程中，熔湯內部溫度及速度場會趨於緩和且晶體長度增加固液界面會更凸向熔湯。不同長晶參數部分，底部絕熱層為氧化鋯球、線圈位置在熔湯中心-10mm與線圈形狀為11組小尺寸線圈，所得到的溫梯與功率都為最低。
最後探討不同長晶階段的最佳化線圈位置，並模擬理想晶體生長過程，其功率與各階段溫梯都有下降的趨勢，對於單晶生長品質與節能方面都有較佳的效果。這些分析結果可作為柴氏長晶系統生長氧化鋁單晶時重要參考指標，並可為將來深入研究單晶生長機制的基礎。

摘要(英)

The thermal and flow transport in a Czochralski crystal growth furnace plays an important role to effect the single crystal growth quality of sapphire. However, the thermal and flow fields in the melt of the single crystal growth process are difficult to observe in experimental study. This thesis has numerically investigated the thermal and flow transport phenomenon using the finite element method via COMSOL Multiphysics software. The electromagnetic, thermal, and fluid fields during the sapphire single crystal growth process have been investigated. The temperature and flow fields inside the furnace are coupled with the heat generation in the Iridium crucible which was generated by the electromagnetic field using the RF coil.
The results presented here demonstrate the effect of different position of coils, different insulator materials of bottom, and different coil forms. The melt temperature and velocity field, power and the temperature gradient distribution during the crystallization have been presented. The results show that the maximum value of the temperature and velocity fields decreases in the melt and the deflection height of the crystal–melt interface increases, as the melt level goes down. In different crystal growth parameter parts, when the ZrO bubble insulator of bottoms is used, the position of coil under the melt center is 10mm and the coil form is 11 groups of small size of coils, the temperature gradient along the crystallization and the input power is lower for the cases considered here. Based on these results, the optimal crystal growth process has been proposed. The results show that the power and the temperature gradient distribution during the crystallization decreases significantly, the single crystal growth quality of sapphire and energy-conservation effect have been improved.

關鍵字(中)

★ CZ法
★ 晶體生長過程
★ 氧化鋁單晶
★ 數值模擬

關鍵字(英)

★ CZ method
★ crystal growth process
★ sapphire
★ computer simulation

論文目次

目錄
摘要……………………………………………………………………………..Ι
Abstract……………………………………………………………….………II
致謝……………………………………………………………….………..…IV
目錄………………………………………………………………………........V
圖目錄…………………………………………………………………...…..VII
表目錄…………………………………………………………...………....….X
符號說明…………………………………………………...…………..…......XI
第一章緒論………………………………………………………………..…1
1.1氧化鋁單晶(Sapphire)簡介…………………………………………….…..1
1.2柴式長晶法(CZ)介紹………………………………………………………2
1.3文獻回顧………………………………………………………………...….3
1.4影響單晶生長參數………………………………………………………....7
1.5研究目的……………………………………………………………..……..8
第二章系統描述與數學模式………………………………………….…12
2.1物理系統與假設……………………………………………………..……12
2.2二維軸對稱模型數學模式…………………………………………..……13
2.2.1電磁場理論分析……………………………………………….....…13
2.2.2熱場理論分析…………………………………………………….....15
2.2.3流場理論分析……………………………………………..……...…19
第三章求解方法與分析步驟………………………………………….…24
3.1 求解方法……………………………………………………………....…24
3.1.1形狀函數……………………………………………………….……24
3.1.2收斂條件……………………………………………………….....…25
3.1.3固化理論………………………………………………………..…...25
3.1.4三場耦合………………………………………………………...…..27
3.1.5由理論基礎判別溶湯流動趨勢……………………………...……..27
3.2長晶模擬分析步驟………………………………………………………..29
3.2.1繪製幾何圖形(Geometry)…………………………………………..30
3.2.2元素型式及材料定義…………………………………………....….30
3.2.3統御條件設定(G.E)與邊界條件設定(B.C) ………………..………30
3.2.4網格與網格測試………………………………………………...…. 30
3.2.5求解與分析…………………………………..……………………...31
第四章結果與討論…………………………………………………..….…38
4.1實際長晶生長過程趨勢驗證…………………………………………..…38
4.1.1實際長晶製程參數……………………………………………….…38
4.1.2實際長晶生長過程模擬分析…………………………………….....39
4.2不同條件參數對長晶過程熱流場分析…………………………………..40
4.2.1坩堝底部絕熱層不同對氧化鋁熔湯的影響…………………….....41
4.2.2維持特定晶體長度時，RF Coil位置不同時的影響…………...…42
4.2.3固定晶體長度時，RF Coil位置不同時的影響…………………...44
4.2.4不同的RF Coil尺寸設計比較…………………………………...…45
4.3 最佳化線圈位置探討……………………………………………………46
4.4 理想長晶過程模擬………………………………………………………47
第五章結論………………………………………………………………...76
參考文獻…………………………………………………………………......78
圖目錄
圖1-1 長晶熱傳遞示意圖…………………..………………..…………….11
圖1-2 柴式長晶爐示意圖………………...…..……..………..…..………..11
圖2-1 長晶爐體內部各元件配置圖…………………………..…….……..21
圖2-2 軸對稱系統主要分析的元件模型……………………...…….…….21
圖2-3 系統邊界條件設定………………………………………………….22
圖2-4 熱輻射示意圖....…………………………………………………….23
圖2-5 各表面視角因子(view factor)示意圖………….……...……….…...23
圖3-1 COMSOL模擬分析流程圖………………………………...…….....34
圖3-2 長晶爐內部元件幾何圖形……...….…………….……….......…….34
圖3-3 非結構網格(三角網格)………………………………………...........35
圖3-4 結構網格(四邊形網格)……………………………………..…..…...35
圖3-5 本系統建立的網格………………………………………………….36
圖3-6 網格測試點………………………………………………...…..36
圖3-7 網格測試溫度圖...………….……………………….….……..…….37
圖4-1 實際長晶過程模擬整體熱場與電磁場分佈………………..…...…54
圖4-2 實際長晶過程模擬熱流場分佈…………….……………..…….…55
圖4-3 熔湯中心軸溫度分佈…………….……………………………..…56
圖4-4 熔湯中心軸速度分佈…………….…………………………..….…56
圖 4-5 晶尾長度定義(h)………….…………………...…………..……….57
圖 4-6 長晶過程各階段晶尾長度…………….……………...…...……….57
圖4-7 功率趨勢比較圖………….………………………….……..….……58
圖4-8 晶體對照圖………….……………………………….……..….……58
圖4-9 固定晶體長度，不同底部絕熱層示意圖………….………………59
圖4-10 不同底部絕熱層中心軸溫度分佈……………..….….…..……...…59
圖4-11不同底部絕熱層晶尾長度……………..………………….…..…60
圖4-12 不同底部絕熱層底部溫度分佈……………..…………….…..……60
圖4-13 不同底部絕熱層溫度分佈圖…………….………………….…...…61
圖4-14 不同底部絕熱層晶體固液介面溫梯分佈……………………….…61
圖4-15 晶柱90mm線圈位置改變示意圖…………….……………….……62
圖4-16 晶柱90mm線圈位置改變電磁場分佈圖…………….……….……62
圖4-17 晶柱90mm線圈位置縱向溫梯分佈圖…………….………….……62
圖4-18 能量傳遞趨勢計算邊界示意圖………….........................................63
圖4-19 晶柱90mm線圈位置不同之晶尾長度…………….………….……63
圖4-20 晶柱90mm線圈位置改變溫度分佈…………….…………….....…64
圖4-21 晶柱90mm線圈位置改變晶體固液介面溫梯分佈…………...…...64
圖4-22 不同晶體長度，線圈位置改變示意圖…………....……………...…65
圖4-23 不同晶體長度，線圈位置改變power趨勢圖…..………….………65
圖4-24 不同晶體長度，線圈位置改變電磁場分佈………….…...……..…66
圖4-25 不同晶體長度，線圈位置不同晶尾長度……..……….……………66
圖4-26 不同晶體長度，線圈位置改變晶體固液介面溫梯……...............…67
圖4-27 線圈形狀尺寸不同示意圖………...………………………..………67
圖4-28 線圈形狀尺寸不同電磁場分佈………….……………..……..……68
圖4-29 線圈形狀尺寸不同晶尾長度………..…………………………...…68
圖4-30 線圈形狀尺寸不同晶體固液介面溫梯……………………….....…69
圖4-31 最佳化線圈位置功率趨勢與晶體固液介面溫梯分佈….…………69
圖4-32 線圈中心離坩堝底部距離示意圖.………..……………………..…70
圖4-33 各階段線圈中心離坩堝底部距離圖……..………....………...……70
圖4-34 不同長晶過程功率趨勢比較圖…………....………………...…..…71
圖4-35 Case2長晶過程整體熱場與電磁場分佈……………………….…72
圖4-36 Case2長晶過程熱流場分佈………….……….……...............……73
圖4-37 Case1與Case2各階段晶體固液介面溫梯……………..…………74
圖4-38 各元件絕熱層熱傳遞趨勢……………………….……..…………75
表目錄
表1-1 氧化鋁單晶特性表……………………………..……….…………..10
表3-1 長晶爐內各元件材料性質…………………………..………….…..33
表3-2 sapphire液體與固體物理特性……………………..……………….33
表4-1 實際長晶過程模擬數據……..………………………..…….………50
表4-2 不同底部絕熱層模擬數據………………..……………..….………50
表4-3 晶體長度90mm，不同線圈位置模擬數據………..…………..…….51
表4-4 不同晶體長度，不同線圈位置模擬數據.………….…....………….51
表4-5 RF線圈尺寸設計不同模擬數據…………………………..…….….52
表4-6 不同長晶過程之線圈位置…………………………………….……52
表4-7 case2長晶模擬數據…..……………………………………….……53
表4-7 不同長晶過程生長階段最高溫位置比較…………..…………...…53

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指導教授

陳志臣(Jyh-Chen Chen)

審核日期

2008-7-23

推文